Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces. (October 2019) - Yang, Fei; Zhang, Liangdi
Abstract: Let ( M n, g, e − ϕ d v ) be a smooth metric measure space. In this paper, we derive a series of gradient estimates and a Harnack inequality for positive solutions of a nonlinear parabolic partial differential equation ( Δ ϕ − ∂ t ) u = q u + a u ( ln u ) α in M n × ( − ∞, + ∞ ), where q ∈ C 2, 1 ( M n × ( − ∞, + ∞ ) ) and a, α ∈ R .